In a conventional vehicle, as an auxiliary battery, a lead battery having a rated voltage of 12V is installed. Further, in a large vehicle, a battery having a rated voltage of 24 V by connecting two of the lead batteries of 12V in series is installed. The lead battery is charged by an alternator in the vehicle, and supplies electric power to auxiliary electrical devices in the vehicle, a starter motor, or the like. This lead battery is heavy and large, and it is necessary to always keep the voltage near the full charge level in order to decrease the degradation and make a life longer. Therefore, the real capacity which is able to be charged and discharged against the rated capacity is small.
Further, when the lead battery is installed in the vehicle having an idle stop function, a life of the battery is remarkably shortened, for example, the life becomes less than a half. Its reason is in the following. In the lead battery charged by power of a regenerative power generation, the voltage of the lead battery is not kept at a constant voltage by an alternator, which is actuated by an engine. The lead battery is charged with very large current at the time of regenerative braking. When the lead battery and alternator supplies electric power to auxiliary electrical devices, the lead battery is not kept at a constant voltage with charging by the alternator. Namely the lead battery does not become in a so-called flouting charge state, the battery voltage is widely varied. As a result, the lead battery is degraded. As a battery system to improve this demerit, a battery system for a vehicle in which the lead battery is connected in parallel to a sub-battery, for example, a nickel hydride battery, a lithium ion secondary battery, or the like, has been developed. (refer to patent literature 1)